(172g) Output Feedback Control of Integrated Lumped and Distributed Parameter Systems Using Mobile Sensors Network

The optimal control and real-time decision-making are often implemented in the chemical process industry with model predictive control (MPC), due to its relative simplicity, flexibility, performance, robustness, and its ability to efficiently handle complex multivariable systems with the hard path and terminal constraints [1]. MPC addresses the control problem by repeatedly solving a constrained dynamic optimization problem to compute a sequence of future manipulated inputs. Since the availability of full state information at each sampling time cannot be invoked in practical cases, using a state estimation method is required along with the control algorithm. Among the several available methods for state estimation, moving horizon estimation (MHE) has attracted much attention because it can be formulated as a similar constrained dynamic optimization problem [2-5].

Complex chemical plants can be considered as integrated networks of lumped parameter systems (LPSs) (e.g., staged separators, well-mixed reactors), described by ordinary differential equations (ODEs) and distributed parameter systems (DPSs) (e.g., tubular reactors, packed beds, heat exchangers) described by partial differential equations (PDEs) [6, 7]. For such systems of systems, the solvability of the MHE and MPC becomes more crucial because the underlying optimization problem must be solved in the presence of PDE constraints involving spatial variation and complex temporal dynamics of the state variables [7].

This work focuses on developing an algorithmic framework to address the nonlinear output-feedback control problem for integrated LPSs and DPSs through a combined MHE and MPC. Reduced-order model representations of the PDEs in the form of finite-dimensional ODEs are employed as the basis for the dynamic optimization formulation in the estimation and control problems. A network of mobile sensors that provide continuous measurement outputs is used to improve the MHE performance in estimating the spatial profiles of the system states. The mobile sensors are capable of moving within spatial domains of the DPSs. The basic premise of this proposed method is that a set of mobile sensors achieve better estimation performance than a set of fixed sensors [8]. The effectiveness of the proposed combined MHE and MPC is demonstrated through a case study on a benchmark diffusion-convection-reaction process network. The estimation error and the closed-loop performance are evaluated using detailed simulations for the spatially distributed fixed and mobile sensors, as well as for different scanning speeds of the mobile sensors to propose a scanning policy.

1. Rawlings, J. B.; Mayne, D. Q.; Diehl, M. Model Predictive Control: Theory, Computation, And Design; Nob Hill Publishing: Madison, WI, 2017.
2. Copp, D.; Hespanha, J. Simultaneous nonlinear model predictive control and state estimation. Automatica 2017, 77, 143-154.
3. Rawlings, J.; Bakshi, B. Particle filtering and moving horizon estimation. Comput. Chem. Eng. 2006, 30(10-12), 1529-1541.
4. Rao, C. V.; Rawlings, J. B.; Mayne, D. Q. Constrained state estimation for nonlinear discrete-time systems: Stability and moving horizon approximations. IEEE Trans. Autom. Control 2003, 48(2), 246-258.
5. Pourkargar, D. B.; Moharir, M.; Almansoori, A.; Daoutidis, P. Distributed estimation and nonlinear model predictive control using community detection. Ind. Eng. Chem. Res. 2019, 58, 13495-13507.
6. Christofides, P.D. Nonlinear and robust control of PDE systems; Birkhauser: New York, NY, 2000.
7. Moharir, M.; Pourkargar, D. B.; Almansoori, A.; Daoutidis, P. Graph representation and distributed control of diffusion-convection-reaction system networks. Chem. Eng. Sci. 2019, 204, 128-139.
8. Demetriou, M.A.; Hussein, I.I. Estimation of spatially distributed processes using mobile spatially distributed sensor network. SIAM J. Control Optim. 2009, 48(1), 266-291.